Functional representation for fermionic quantum fields

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Abstract
A functional representation for fermionic quantum fields is developed in analogy to familiar results for bosonic fields. The infinite Clifford algebra of the field anticommutator is realized reducibly on a Grassmann functional space. On this space, transformation groups may be represented without normal ordering with respect to a Fock vacuum, and a projective representation for the two-dimensional conformal group is found, which is compared to the corresponding representation in terms of bosonic fields. When a quadratic Hamiltonian for the Fermi fields is posited, a Fock space can be constructed after a prescription for filling the Dirac sea is selected. Different filling prescriptions lead to inequivalent Fock spaces within the functional space. Explicit eigenfunctionals exhibit the peculiarities of fermionic field theory, such as fractional charge, Berry’s phase, and anomalies.

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